<?php
    /** PHPExcel root directory */
    if (!defined('PHPEXCEL_ROOT')) {
        /**
         * @ignore
         */
        define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
        require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
    }
    /** FINANCIAL_MAX_ITERATIONS */
    define('FINANCIAL_MAX_ITERATIONS', 128);
    /** FINANCIAL_PRECISION */
    define('FINANCIAL_PRECISION', 1.0e-08);

    /**
     * PHPExcel_Calculation_Financial
     * Copyright (c) 2006 - 2015 PHPExcel
     * This library is free software; you can redistribute it and/or
     * modify it under the terms of the GNU Lesser General Public
     * License as published by the Free Software Foundation; either
     * version 2.1 of the License, or (at your option) any later version.
     * This library is distributed in the hope that it will be useful,
     * but WITHOUT ANY WARRANTY; without even the implied warranty of
     * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
     * Lesser General Public License for more details.
     * You should have received a copy of the GNU Lesser General Public
     * License along with this library; if not, write to the Free Software
     * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
     * @category       PHPExcel
     * @package        PHPExcel_Calculation
     * @copyright      Copyright (c) 2006 - 2015 PHPExcel (http://www.codeplex.com/PHPExcel)
     * @license        http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
     * @version        ##VERSION##, ##DATE##
     */
    class PHPExcel_Calculation_Financial {
        /**
         * ACCRINT
         * Returns the accrued interest for a security that pays periodic interest.
         * Excel Function:
         *        ACCRINT(issue,firstinterest,settlement,rate,par,frequency[,basis])
         * @access    public
         * @category  Financial Functions
         * @param    mixed   $issue               The security's issue date.
         * @param    mixed   $firstinterest       The security's first interest date.
         * @param    mixed   $settlement          The security's settlement date.
         *                                        The security settlement date is the date after the issue date
         *                                        when the security is traded to the buyer.
         * @param    float   $rate                The security's annual coupon rate.
         * @param    float   $par                 The security's par value.
         *                                        If you omit par, ACCRINT uses $1,000.
         * @param    integer $frequency           the number of coupon payments per year.
         *                                        Valid frequency values are:
         *                                        1    Annual
         *                                        2    Semi-Annual
         *                                        4    Quarterly
         *                                        If working in Gnumeric Mode, the following frequency options are
         *                                        also available
         *                                        6    Bimonthly
         *                                        12    Monthly
         * @param    integer $basis               The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function ACCRINT($issue, $firstinterest, $settlement, $rate, $par = 1000, $frequency = 1, $basis = 0) {
            $issue         = PHPExcel_Calculation_Functions::flattenSingleValue($issue);
            $firstinterest = PHPExcel_Calculation_Functions::flattenSingleValue($firstinterest);
            $settlement    = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $rate          = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $par           = (is_null($par)) ? 1000 : PHPExcel_Calculation_Functions::flattenSingleValue($par);
            $frequency     = (is_null($frequency)) ? 1 : PHPExcel_Calculation_Functions::flattenSingleValue($frequency);
            $basis         = (is_null($basis)) ? 0 : PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            //    Validate
            if ((is_numeric($rate)) && (is_numeric($par))) {
                $rate = (float)$rate;
                $par  = (float)$par;
                if (($rate <= 0) || ($par <= 0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $daysBetweenIssueAndSettlement = PHPExcel_Calculation_DateTime::YEARFRAC($issue, $settlement, $basis);
                if (!is_numeric($daysBetweenIssueAndSettlement)) {
                    //    return date error
                    return $daysBetweenIssueAndSettlement;
                }
                return $par * $rate * $daysBetweenIssueAndSettlement;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * ACCRINTM
         * Returns the accrued interest for a security that pays interest at maturity.
         * Excel Function:
         *        ACCRINTM(issue,settlement,rate[,par[,basis]])
         * @access    public
         * @category  Financial Functions
         * @param    mixed                        issue        The security's issue date.
         * @param    mixed                        settlement    The security's settlement (or maturity) date.
         * @param    float                        rate        The security's annual coupon rate.
         * @param    float                        par            The security's par value.
         *                                        If you omit par, ACCRINT uses $1,000.
         * @param    integer                      basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function ACCRINTM($issue, $settlement, $rate, $par = 1000, $basis = 0) {
            $issue      = PHPExcel_Calculation_Functions::flattenSingleValue($issue);
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $rate       = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $par        = (is_null($par)) ? 1000 : PHPExcel_Calculation_Functions::flattenSingleValue($par);
            $basis      = (is_null($basis)) ? 0 : PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            //    Validate
            if ((is_numeric($rate)) && (is_numeric($par))) {
                $rate = (float)$rate;
                $par  = (float)$par;
                if (($rate <= 0) || ($par <= 0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $daysBetweenIssueAndSettlement = PHPExcel_Calculation_DateTime::YEARFRAC($issue, $settlement, $basis);
                if (!is_numeric($daysBetweenIssueAndSettlement)) {
                    //    return date error
                    return $daysBetweenIssueAndSettlement;
                }
                return $par * $rate * $daysBetweenIssueAndSettlement;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * AMORDEGRC
         * Returns the depreciation for each accounting period.
         * This function is provided for the French accounting system. If an asset is purchased in
         * the middle of the accounting period, the prorated depreciation is taken into account.
         * The function is similar to AMORLINC, except that a depreciation coefficient is applied in
         * the calculation depending on the life of the assets.
         * This function will return the depreciation until the last period of the life of the assets
         * or until the cumulated value of depreciation is greater than the cost of the assets minus
         * the salvage value.
         * Excel Function:
         *        AMORDEGRC(cost,purchased,firstPeriod,salvage,period,rate[,basis])
         * @access    public
         * @category  Financial Functions
         * @param    float                        cost        The cost of the asset.
         * @param    mixed                        purchased    Date of the purchase of the asset.
         * @param    mixed                        firstPeriod    Date of the end of the first period.
         * @param    mixed                        salvage        The salvage value at the end of the life of the asset.
         * @param    float                        period        The period.
         * @param    float                        rate        Rate of depreciation.
         * @param    integer                      basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function AMORDEGRC($cost, $purchased, $firstPeriod, $salvage, $period, $rate, $basis = 0) {
            $cost        = PHPExcel_Calculation_Functions::flattenSingleValue($cost);
            $purchased   = PHPExcel_Calculation_Functions::flattenSingleValue($purchased);
            $firstPeriod = PHPExcel_Calculation_Functions::flattenSingleValue($firstPeriod);
            $salvage     = PHPExcel_Calculation_Functions::flattenSingleValue($salvage);
            $period      = floor(PHPExcel_Calculation_Functions::flattenSingleValue($period));
            $rate        = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $basis       = (is_null($basis)) ? 0 : (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            //    The depreciation coefficients are:
            //    Life of assets (1/rate)        Depreciation coefficient
            //    Less than 3 years            1
            //    Between 3 and 4 years        1.5
            //    Between 5 and 6 years        2
            //    More than 6 years            2.5
            $fUsePer = 1.0 / $rate;
            if ($fUsePer < 3.0) {
                $amortiseCoeff = 1.0;
            } elseif ($fUsePer < 5.0) {
                $amortiseCoeff = 1.5;
            } elseif ($fUsePer <= 6.0) {
                $amortiseCoeff = 2.0;
            } else {
                $amortiseCoeff = 2.5;
            }
            $rate   *= $amortiseCoeff;
            $fNRate = round(PHPExcel_Calculation_DateTime::YEARFRAC($purchased, $firstPeriod, $basis) * $rate * $cost, 0);
            $cost   -= $fNRate;
            $fRest  = $cost - $salvage;
            for ($n = 0; $n < $period; ++$n) {
                $fNRate = round($rate * $cost, 0);
                $fRest  -= $fNRate;
                if ($fRest < 0.0) {
                    switch ($period - $n) {
                        case 0:
                        case 1:
                            return round($cost * 0.5, 0);
                        default:
                            return 0.0;
                    }
                }
                $cost -= $fNRate;
            }
            return $fNRate;
        }

        /**
         * AMORLINC
         * Returns the depreciation for each accounting period.
         * This function is provided for the French accounting system. If an asset is purchased in
         * the middle of the accounting period, the prorated depreciation is taken into account.
         * Excel Function:
         *        AMORLINC(cost,purchased,firstPeriod,salvage,period,rate[,basis])
         * @access    public
         * @category  Financial Functions
         * @param    float                        cost        The cost of the asset.
         * @param    mixed                        purchased    Date of the purchase of the asset.
         * @param    mixed                        firstPeriod    Date of the end of the first period.
         * @param    mixed                        salvage        The salvage value at the end of the life of the asset.
         * @param    float                        period        The period.
         * @param    float                        rate        Rate of depreciation.
         * @param    integer                      basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function AMORLINC($cost, $purchased, $firstPeriod, $salvage, $period, $rate, $basis = 0) {
            $cost        = PHPExcel_Calculation_Functions::flattenSingleValue($cost);
            $purchased   = PHPExcel_Calculation_Functions::flattenSingleValue($purchased);
            $firstPeriod = PHPExcel_Calculation_Functions::flattenSingleValue($firstPeriod);
            $salvage     = PHPExcel_Calculation_Functions::flattenSingleValue($salvage);
            $period      = PHPExcel_Calculation_Functions::flattenSingleValue($period);
            $rate        = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $basis       = (is_null($basis)) ? 0 : (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            $fOneRate   = $cost * $rate;
            $fCostDelta = $cost - $salvage;
            //    Note, quirky variation for leap years on the YEARFRAC for this function
            $purchasedYear = PHPExcel_Calculation_DateTime::YEAR($purchased);
            $yearFrac      = PHPExcel_Calculation_DateTime::YEARFRAC($purchased, $firstPeriod, $basis);
            if (($basis == 1) && ($yearFrac < 1) && (PHPExcel_Calculation_DateTime::isLeapYear($purchasedYear))) {
                $yearFrac *= 365 / 366;
            }
            $f0Rate            = $yearFrac * $rate * $cost;
            $nNumOfFullPeriods = intval(($cost - $salvage - $f0Rate) / $fOneRate);
            if ($period == 0) {
                return $f0Rate;
            } elseif ($period <= $nNumOfFullPeriods) {
                return $fOneRate;
            } elseif ($period == ($nNumOfFullPeriods + 1)) {
                return ($fCostDelta - $fOneRate * $nNumOfFullPeriods - $f0Rate);
            } else {
                return 0.0;
            }
        }

        /**
         * COUPNCD
         * Returns the next coupon date after the settlement date.
         * Excel Function:
         *        COUPNCD(settlement,maturity,frequency[,basis])
         * @access    public
         * @category  Financial Functions
         * @param    mixed                        settlement    The security's settlement date.
         *                                        The security settlement date is the date after the issue
         *                                        date when the security is traded to the buyer.
         * @param    mixed                        maturity    The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    mixed                        frequency    the number of coupon payments per year.
         *                                        Valid frequency values are:
         *                                        1    Annual
         *                                        2    Semi-Annual
         *                                        4    Quarterly
         *                                        If working in Gnumeric Mode, the following frequency options are
         *                                        also available
         *                                        6    Bimonthly
         *                                        12    Monthly
         * @param    integer                      basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    mixed    Excel date/time serial value, PHP date/time serial value or PHP date/time object,
         *                                        depending on the value of the ReturnDateType flag
         */
        public static function COUPNCD($settlement, $maturity, $frequency, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $frequency  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($frequency);
            $basis      = (is_null($basis)) ? 0 : (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            if (is_string($settlement = PHPExcel_Calculation_DateTime::getDateValue($settlement))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (is_string($maturity = PHPExcel_Calculation_DateTime::getDateValue($maturity))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (($settlement > $maturity) || (!self::isValidFrequency($frequency)) || (($basis < 0) || ($basis > 4))) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return self::couponFirstPeriodDate($settlement, $maturity, $frequency, true);
        }

        private static function isValidFrequency($frequency) {
            if (($frequency == 1) || ($frequency == 2) || ($frequency == 4)) {
                return true;
            }
            if ((PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) && (($frequency == 6) || ($frequency == 12))) {
                return true;
            }
            return false;
        }

        private static function couponFirstPeriodDate($settlement, $maturity, $frequency, $next) {
            $months = 12 / $frequency;
            $result = PHPExcel_Shared_Date::ExcelToPHPObject($maturity);
            $eom    = self::isLastDayOfMonth($result);
            while ($settlement < PHPExcel_Shared_Date::PHPToExcel($result)) {
                $result->modify('-' . $months . ' months');
            }
            if ($next) {
                $result->modify('+' . $months . ' months');
            }
            if ($eom) {
                $result->modify('-1 day');
            }
            return PHPExcel_Shared_Date::PHPToExcel($result);
        }

        /**
         * isLastDayOfMonth
         * Returns a boolean TRUE/FALSE indicating if this date is the last date of the month
         * @param    DateTime $testDate The date for testing
         * @return    boolean
         */
        private static function isLastDayOfMonth($testDate) {
            return ($testDate->format('d') == $testDate->format('t'));
        }

        /**
         * COUPPCD
         * Returns the previous coupon date before the settlement date.
         * Excel Function:
         *        COUPPCD(settlement,maturity,frequency[,basis])
         * @access    public
         * @category  Financial Functions
         * @param    mixed                        settlement    The security's settlement date.
         *                                        The security settlement date is the date after the issue
         *                                        date when the security is traded to the buyer.
         * @param    mixed                        maturity    The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    mixed                        frequency    the number of coupon payments per year.
         *                                        Valid frequency values are:
         *                                        1    Annual
         *                                        2    Semi-Annual
         *                                        4    Quarterly
         *                                        If working in Gnumeric Mode, the following frequency options are
         *                                        also available
         *                                        6    Bimonthly
         *                                        12    Monthly
         * @param    integer                      basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    mixed    Excel date/time serial value, PHP date/time serial value or PHP date/time object,
         *                                        depending on the value of the ReturnDateType flag
         */
        public static function COUPPCD($settlement, $maturity, $frequency, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $frequency  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($frequency);
            $basis      = (is_null($basis)) ? 0 : (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            if (is_string($settlement = PHPExcel_Calculation_DateTime::getDateValue($settlement))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (is_string($maturity = PHPExcel_Calculation_DateTime::getDateValue($maturity))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (($settlement > $maturity) || (!self::isValidFrequency($frequency)) || (($basis < 0) || ($basis > 4))) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return self::couponFirstPeriodDate($settlement, $maturity, $frequency, false);
        }

        /**
         * CUMIPMT
         * Returns the cumulative interest paid on a loan between the start and end periods.
         * Excel Function:
         *        CUMIPMT(rate,nper,pv,start,end[,type])
         * @access    public
         * @category  Financial Functions
         * @param    float   $rate        The Interest rate
         * @param    integer $nper        The total number of payment periods
         * @param    float   $pv          Present Value
         * @param    integer $start       The first period in the calculation.
         *                                Payment periods are numbered beginning with 1.
         * @param    integer $end         The last period in the calculation.
         * @param    integer $type        A number 0 or 1 and indicates when payments are due:
         *                                0 or omitted    At the end of the period.
         *                                1                At the beginning of the period.
         * @return    float
         */
        public static function CUMIPMT($rate, $nper, $pv, $start, $end, $type = 0) {
            $rate  = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $nper  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($nper);
            $pv    = PHPExcel_Calculation_Functions::flattenSingleValue($pv);
            $start = (int)PHPExcel_Calculation_Functions::flattenSingleValue($start);
            $end   = (int)PHPExcel_Calculation_Functions::flattenSingleValue($end);
            $type  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($type);
            // Validate parameters
            if ($type != 0 && $type != 1) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if ($start < 1 || $start > $end) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            // Calculate
            $interest = 0;
            for ($per = $start; $per <= $end; ++$per) {
                $interest += self::IPMT($rate, $per, $nper, $pv, 0, $type);
            }
            return $interest;
        }

        /**
         * IPMT
         * Returns the interest payment for a given period for an investment based on periodic, constant payments and a constant interest rate.
         * Excel Function:
         *        IPMT(rate,per,nper,pv[,fv][,type])
         * @param    float $rate Interest rate per period
         * @param    int   $per  Period for which we want to find the interest
         * @param    int   $nper Number of periods
         * @param    float $pv   Present Value
         * @param    float $fv   Future Value
         * @param    int   $type Payment type: 0 = at the end of each period, 1 = at the beginning of each period
         * @return    float
         */
        public static function IPMT($rate, $per, $nper, $pv, $fv = 0, $type = 0) {
            $rate = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $per  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($per);
            $nper = (int)PHPExcel_Calculation_Functions::flattenSingleValue($nper);
            $pv   = PHPExcel_Calculation_Functions::flattenSingleValue($pv);
            $fv   = PHPExcel_Calculation_Functions::flattenSingleValue($fv);
            $type = (int)PHPExcel_Calculation_Functions::flattenSingleValue($type);
            // Validate parameters
            if ($type != 0 && $type != 1) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if ($per <= 0 || $per > $nper) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            // Calculate
            $interestAndPrincipal = self::interestAndPrincipal($rate, $per, $nper, $pv, $fv, $type);
            return $interestAndPrincipal[0];
        }

        private static function interestAndPrincipal($rate = 0, $per = 0, $nper = 0, $pv = 0, $fv = 0, $type = 0) {
            $pmt     = self::PMT($rate, $nper, $pv, $fv, $type);
            $capital = $pv;
            for ($i = 1; $i <= $per; ++$i) {
                $interest  = ($type && $i == 1) ? 0 : -$capital * $rate;
                $principal = $pmt - $interest;
                $capital   += $principal;
            }
            return [
                $interest,
                $principal
            ];
        }

        /**
         * PMT
         * Returns the constant payment (annuity) for a cash flow with a constant interest rate.
         * @param    float $rate Interest rate per period
         * @param    int   $nper Number of periods
         * @param    float $pv   Present Value
         * @param    float $fv   Future Value
         * @param    int   $type Payment type: 0 = at the end of each period, 1 = at the beginning of each period
         * @return    float
         */
        public static function PMT($rate = 0, $nper = 0, $pv = 0, $fv = 0, $type = 0) {
            $rate = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $nper = PHPExcel_Calculation_Functions::flattenSingleValue($nper);
            $pv   = PHPExcel_Calculation_Functions::flattenSingleValue($pv);
            $fv   = PHPExcel_Calculation_Functions::flattenSingleValue($fv);
            $type = PHPExcel_Calculation_Functions::flattenSingleValue($type);
            // Validate parameters
            if ($type != 0 && $type != 1) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            // Calculate
            if (!is_null($rate) && $rate != 0) {
                return (-$fv - $pv * pow(1 + $rate, $nper)) / (1 + $rate * $type) / ((pow(1 + $rate, $nper) - 1) / $rate);
            }
            return (-$pv - $fv) / $nper;
        }

        /**
         * CUMPRINC
         * Returns the cumulative principal paid on a loan between the start and end periods.
         * Excel Function:
         *        CUMPRINC(rate,nper,pv,start,end[,type])
         * @access    public
         * @category  Financial Functions
         * @param    float   $rate        The Interest rate
         * @param    integer $nper        The total number of payment periods
         * @param    float   $pv          Present Value
         * @param    integer $start       The first period in the calculation.
         *                                Payment periods are numbered beginning with 1.
         * @param    integer $end         The last period in the calculation.
         * @param    integer $type        A number 0 or 1 and indicates when payments are due:
         *                                0 or omitted    At the end of the period.
         *                                1                At the beginning of the period.
         * @return    float
         */
        public static function CUMPRINC($rate, $nper, $pv, $start, $end, $type = 0) {
            $rate  = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $nper  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($nper);
            $pv    = PHPExcel_Calculation_Functions::flattenSingleValue($pv);
            $start = (int)PHPExcel_Calculation_Functions::flattenSingleValue($start);
            $end   = (int)PHPExcel_Calculation_Functions::flattenSingleValue($end);
            $type  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($type);
            // Validate parameters
            if ($type != 0 && $type != 1) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if ($start < 1 || $start > $end) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            // Calculate
            $principal = 0;
            for ($per = $start; $per <= $end; ++$per) {
                $principal += self::PPMT($rate, $per, $nper, $pv, 0, $type);
            }
            return $principal;
        }

        /**
         * PPMT
         * Returns the interest payment for a given period for an investment based on periodic, constant payments and a constant interest rate.
         * @param    float $rate Interest rate per period
         * @param    int   $per  Period for which we want to find the interest
         * @param    int   $nper Number of periods
         * @param    float $pv   Present Value
         * @param    float $fv   Future Value
         * @param    int   $type Payment type: 0 = at the end of each period, 1 = at the beginning of each period
         * @return    float
         */
        public static function PPMT($rate, $per, $nper, $pv, $fv = 0, $type = 0) {
            $rate = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $per  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($per);
            $nper = (int)PHPExcel_Calculation_Functions::flattenSingleValue($nper);
            $pv   = PHPExcel_Calculation_Functions::flattenSingleValue($pv);
            $fv   = PHPExcel_Calculation_Functions::flattenSingleValue($fv);
            $type = (int)PHPExcel_Calculation_Functions::flattenSingleValue($type);
            // Validate parameters
            if ($type != 0 && $type != 1) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if ($per <= 0 || $per > $nper) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            // Calculate
            $interestAndPrincipal = self::interestAndPrincipal($rate, $per, $nper, $pv, $fv, $type);
            return $interestAndPrincipal[1];
        }

        /**
         * DB
         * Returns the depreciation of an asset for a specified period using the
         * fixed-declining balance method.
         * This form of depreciation is used if you want to get a higher depreciation value
         * at the beginning of the depreciation (as opposed to linear depreciation). The
         * depreciation value is reduced with every depreciation period by the depreciation
         * already deducted from the initial cost.
         * Excel Function:
         *        DB(cost,salvage,life,period[,month])
         * @access    public
         * @category  Financial Functions
         * @param    float                cost        Initial cost of the asset.
         * @param    float                salvage        Value at the end of the depreciation.
         *                                (Sometimes called the salvage value of the asset)
         * @param    integer              life        Number of periods over which the asset is depreciated.
         *                                (Sometimes called the useful life of the asset)
         * @param    integer              period        The period for which you want to calculate the
         *                                depreciation. Period must use the same units as life.
         * @param    integer              month        Number of months in the first year. If month is omitted,
         *                                it defaults to 12.
         * @return    float
         */
        public static function DB($cost, $salvage, $life, $period, $month = 12) {
            $cost    = PHPExcel_Calculation_Functions::flattenSingleValue($cost);
            $salvage = PHPExcel_Calculation_Functions::flattenSingleValue($salvage);
            $life    = PHPExcel_Calculation_Functions::flattenSingleValue($life);
            $period  = PHPExcel_Calculation_Functions::flattenSingleValue($period);
            $month   = PHPExcel_Calculation_Functions::flattenSingleValue($month);
            //    Validate
            if ((is_numeric($cost)) && (is_numeric($salvage)) && (is_numeric($life)) && (is_numeric($period)) && (is_numeric($month))) {
                $cost    = (float)$cost;
                $salvage = (float)$salvage;
                $life    = (int)$life;
                $period  = (int)$period;
                $month   = (int)$month;
                if ($cost == 0) {
                    return 0.0;
                } elseif (($cost < 0) || (($salvage / $cost) < 0) || ($life <= 0) || ($period < 1) || ($month < 1)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                //    Set Fixed Depreciation Rate
                $fixedDepreciationRate = 1 - pow(($salvage / $cost), (1 / $life));
                $fixedDepreciationRate = round($fixedDepreciationRate, 3);
                //    Loop through each period calculating the depreciation
                $previousDepreciation = 0;
                for ($per = 1; $per <= $period; ++$per) {
                    if ($per == 1) {
                        $depreciation = $cost * $fixedDepreciationRate * $month / 12;
                    } elseif ($per == ($life + 1)) {
                        $depreciation = ($cost - $previousDepreciation) * $fixedDepreciationRate * (12 - $month) / 12;
                    } else {
                        $depreciation = ($cost - $previousDepreciation) * $fixedDepreciationRate;
                    }
                    $previousDepreciation += $depreciation;
                }
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
                    $depreciation = round($depreciation, 2);
                }
                return $depreciation;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * DDB
         * Returns the depreciation of an asset for a specified period using the
         * double-declining balance method or some other method you specify.
         * Excel Function:
         *        DDB(cost,salvage,life,period[,factor])
         * @access    public
         * @category  Financial Functions
         * @param    float                cost        Initial cost of the asset.
         * @param    float                salvage        Value at the end of the depreciation.
         *                                (Sometimes called the salvage value of the asset)
         * @param    integer              life        Number of periods over which the asset is depreciated.
         *                                (Sometimes called the useful life of the asset)
         * @param    integer              period        The period for which you want to calculate the
         *                                depreciation. Period must use the same units as life.
         * @param    float                factor        The rate at which the balance declines.
         *                                If factor is omitted, it is assumed to be 2 (the
         *                                double-declining balance method).
         * @return    float
         */
        public static function DDB($cost, $salvage, $life, $period, $factor = 2.0) {
            $cost    = PHPExcel_Calculation_Functions::flattenSingleValue($cost);
            $salvage = PHPExcel_Calculation_Functions::flattenSingleValue($salvage);
            $life    = PHPExcel_Calculation_Functions::flattenSingleValue($life);
            $period  = PHPExcel_Calculation_Functions::flattenSingleValue($period);
            $factor  = PHPExcel_Calculation_Functions::flattenSingleValue($factor);
            //    Validate
            if ((is_numeric($cost)) && (is_numeric($salvage)) && (is_numeric($life)) && (is_numeric($period)) && (is_numeric($factor))) {
                $cost    = (float)$cost;
                $salvage = (float)$salvage;
                $life    = (int)$life;
                $period  = (int)$period;
                $factor  = (float)$factor;
                if (($cost <= 0) || (($salvage / $cost) < 0) || ($life <= 0) || ($period < 1) || ($factor <= 0.0) || ($period > $life)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                //    Set Fixed Depreciation Rate
                $fixedDepreciationRate = 1 - pow(($salvage / $cost), (1 / $life));
                $fixedDepreciationRate = round($fixedDepreciationRate, 3);
                //    Loop through each period calculating the depreciation
                $previousDepreciation = 0;
                for ($per = 1; $per <= $period; ++$per) {
                    $depreciation         = min(($cost - $previousDepreciation) * ($factor / $life), ($cost - $salvage - $previousDepreciation));
                    $previousDepreciation += $depreciation;
                }
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
                    $depreciation = round($depreciation, 2);
                }
                return $depreciation;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * DISC
         * Returns the discount rate for a security.
         * Excel Function:
         *        DISC(settlement,maturity,price,redemption[,basis])
         * @access    public
         * @category  Financial Functions
         * @param    mixed                        settlement    The security's settlement date.
         *                                        The security settlement date is the date after the issue
         *                                        date when the security is traded to the buyer.
         * @param    mixed                        maturity    The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    integer                      price        The security's price per $100 face value.
         * @param    integer                      redemption    The security's redemption value per $100 face value.
         * @param    integer                      basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function DISC($settlement, $maturity, $price, $redemption, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $price      = PHPExcel_Calculation_Functions::flattenSingleValue($price);
            $redemption = PHPExcel_Calculation_Functions::flattenSingleValue($redemption);
            $basis      = PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            //    Validate
            if ((is_numeric($price)) && (is_numeric($redemption)) && (is_numeric($basis))) {
                $price      = (float)$price;
                $redemption = (float)$redemption;
                $basis      = (int)$basis;
                if (($price <= 0) || ($redemption <= 0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity, $basis);
                if (!is_numeric($daysBetweenSettlementAndMaturity)) {
                    //    return date error
                    return $daysBetweenSettlementAndMaturity;
                }
                return ((1 - $price / $redemption) / $daysBetweenSettlementAndMaturity);
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * DOLLARDE
         * Converts a dollar price expressed as an integer part and a fraction
         *        part into a dollar price expressed as a decimal number.
         * Fractional dollar numbers are sometimes used for security prices.
         * Excel Function:
         *        DOLLARDE(fractional_dollar,fraction)
         * @access    public
         * @category  Financial Functions
         * @param    float   $fractional_dollar Fractional Dollar
         * @param    integer $fraction          Fraction
         * @return    float
         */
        public static function DOLLARDE($fractional_dollar = null, $fraction = 0) {
            $fractional_dollar = PHPExcel_Calculation_Functions::flattenSingleValue($fractional_dollar);
            $fraction          = (int)PHPExcel_Calculation_Functions::flattenSingleValue($fraction);
            // Validate parameters
            if (is_null($fractional_dollar) || $fraction < 0) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if ($fraction == 0) {
                return PHPExcel_Calculation_Functions::DIV0();
            }
            $dollars = floor($fractional_dollar);
            $cents   = fmod($fractional_dollar, 1);
            $cents   /= $fraction;
            $cents   *= pow(10, ceil(log10($fraction)));
            return $dollars + $cents;
        }

        /**
         * DOLLARFR
         * Converts a dollar price expressed as a decimal number into a dollar price
         *        expressed as a fraction.
         * Fractional dollar numbers are sometimes used for security prices.
         * Excel Function:
         *        DOLLARFR(decimal_dollar,fraction)
         * @access    public
         * @category  Financial Functions
         * @param    float   $decimal_dollar Decimal Dollar
         * @param    integer $fraction       Fraction
         * @return    float
         */
        public static function DOLLARFR($decimal_dollar = null, $fraction = 0) {
            $decimal_dollar = PHPExcel_Calculation_Functions::flattenSingleValue($decimal_dollar);
            $fraction       = (int)PHPExcel_Calculation_Functions::flattenSingleValue($fraction);
            // Validate parameters
            if (is_null($decimal_dollar) || $fraction < 0) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if ($fraction == 0) {
                return PHPExcel_Calculation_Functions::DIV0();
            }
            $dollars = floor($decimal_dollar);
            $cents   = fmod($decimal_dollar, 1);
            $cents   *= $fraction;
            $cents   *= pow(10, -ceil(log10($fraction)));
            return $dollars + $cents;
        }

        /**
         * EFFECT
         * Returns the effective interest rate given the nominal rate and the number of
         *        compounding payments per year.
         * Excel Function:
         *        EFFECT(nominal_rate,npery)
         * @access    public
         * @category  Financial Functions
         * @param    float   $nominal_rate Nominal interest rate
         * @param    integer $npery        Number of compounding payments per year
         * @return    float
         */
        public static function EFFECT($nominal_rate = 0, $npery = 0) {
            $nominal_rate = PHPExcel_Calculation_Functions::flattenSingleValue($nominal_rate);
            $npery        = (int)PHPExcel_Calculation_Functions::flattenSingleValue($npery);
            // Validate parameters
            if ($nominal_rate <= 0 || $npery < 1) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return pow((1 + $nominal_rate / $npery), $npery) - 1;
        }

        /**
         * FV
         * Returns the Future Value of a cash flow with constant payments and interest rate (annuities).
         * Excel Function:
         *        FV(rate,nper,pmt[,pv[,type]])
         * @access    public
         * @category  Financial Functions
         * @param    float   $rate        The interest rate per period
         * @param    int     $nper        Total number of payment periods in an annuity
         * @param    float   $pmt         The payment made each period: it cannot change over the
         *                                life of the annuity. Typically, pmt contains principal
         *                                and interest but no other fees or taxes.
         * @param    float   $pv          Present Value, or the lump-sum amount that a series of
         *                                future payments is worth right now.
         * @param    integer $type        A number 0 or 1 and indicates when payments are due:
         *                                0 or omitted    At the end of the period.
         *                                1                At the beginning of the period.
         * @return    float
         */
        public static function FV($rate = 0, $nper = 0, $pmt = 0, $pv = 0, $type = 0) {
            $rate = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $nper = PHPExcel_Calculation_Functions::flattenSingleValue($nper);
            $pmt  = PHPExcel_Calculation_Functions::flattenSingleValue($pmt);
            $pv   = PHPExcel_Calculation_Functions::flattenSingleValue($pv);
            $type = PHPExcel_Calculation_Functions::flattenSingleValue($type);
            // Validate parameters
            if ($type != 0 && $type != 1) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            // Calculate
            if (!is_null($rate) && $rate != 0) {
                return -$pv * pow(1 + $rate, $nper) - $pmt * (1 + $rate * $type) * (pow(1 + $rate, $nper) - 1) / $rate;
            }
            return -$pv - $pmt * $nper;
        }

        /**
         * FVSCHEDULE
         * Returns the future value of an initial principal after applying a series of compound interest rates.
         * Use FVSCHEDULE to calculate the future value of an investment with a variable or adjustable rate.
         * Excel Function:
         *        FVSCHEDULE(principal,schedule)
         * @param    float   $principal The present value.
         * @param    float[] $schedule  An array of interest rates to apply.
         * @return    float
         */
        public static function FVSCHEDULE($principal, $schedule) {
            $principal = PHPExcel_Calculation_Functions::flattenSingleValue($principal);
            $schedule  = PHPExcel_Calculation_Functions::flattenArray($schedule);
            foreach ($schedule as $rate) {
                $principal *= 1 + $rate;
            }
            return $principal;
        }

        /**
         * INTRATE
         * Returns the interest rate for a fully invested security.
         * Excel Function:
         *        INTRATE(settlement,maturity,investment,redemption[,basis])
         * @param    mixed   $settlement          The security's settlement date.
         *                                        The security settlement date is the date after the issue date when the security is traded to the buyer.
         * @param    mixed   $maturity            The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    integer $investment          The amount invested in the security.
         * @param    integer $redemption          The amount to be received at maturity.
         * @param    integer $basis               The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function INTRATE($settlement, $maturity, $investment, $redemption, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $investment = PHPExcel_Calculation_Functions::flattenSingleValue($investment);
            $redemption = PHPExcel_Calculation_Functions::flattenSingleValue($redemption);
            $basis      = PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            //    Validate
            if ((is_numeric($investment)) && (is_numeric($redemption)) && (is_numeric($basis))) {
                $investment = (float)$investment;
                $redemption = (float)$redemption;
                $basis      = (int)$basis;
                if (($investment <= 0) || ($redemption <= 0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity, $basis);
                if (!is_numeric($daysBetweenSettlementAndMaturity)) {
                    //    return date error
                    return $daysBetweenSettlementAndMaturity;
                }
                return (($redemption / $investment) - 1) / ($daysBetweenSettlementAndMaturity);
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * IRR
         * Returns the internal rate of return for a series of cash flows represented by the numbers in values.
         * These cash flows do not have to be even, as they would be for an annuity. However, the cash flows must occur
         * at regular intervals, such as monthly or annually. The internal rate of return is the interest rate received
         * for an investment consisting of payments (negative values) and income (positive values) that occur at regular
         * periods.
         * Excel Function:
         *        IRR(values[,guess])
         * @param    float[] $values          An array or a reference to cells that contain numbers for which you want
         *                                    to calculate the internal rate of return.
         *                                    Values must contain at least one positive value and one negative value to
         *                                    calculate the internal rate of return.
         * @param    float   $guess           A number that you guess is close to the result of IRR
         * @return    float
         */
        public static function IRR($values, $guess = 0.1) {
            if (!is_array($values)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $values = PHPExcel_Calculation_Functions::flattenArray($values);
            $guess  = PHPExcel_Calculation_Functions::flattenSingleValue($guess);
            // create an initial range, with a root somewhere between 0 and guess
            $x1 = 0.0;
            $x2 = $guess;
            $f1 = self::NPV($x1, $values);
            $f2 = self::NPV($x2, $values);
            for ($i = 0; $i < FINANCIAL_MAX_ITERATIONS; ++$i) {
                if (($f1 * $f2) < 0.0) {
                    break;
                }
                if (abs($f1) < abs($f2)) {
                    $f1 = self::NPV($x1 += 1.6 * ($x1 - $x2), $values);
                } else {
                    $f2 = self::NPV($x2 += 1.6 * ($x2 - $x1), $values);
                }
            }
            if (($f1 * $f2) > 0.0) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $f = self::NPV($x1, $values);
            if ($f < 0.0) {
                $rtb = $x1;
                $dx  = $x2 - $x1;
            } else {
                $rtb = $x2;
                $dx  = $x1 - $x2;
            }
            for ($i = 0; $i < FINANCIAL_MAX_ITERATIONS; ++$i) {
                $dx    *= 0.5;
                $x_mid = $rtb + $dx;
                $f_mid = self::NPV($x_mid, $values);
                if ($f_mid <= 0.0) {
                    $rtb = $x_mid;
                }
                if ((abs($f_mid) < FINANCIAL_PRECISION) || (abs($dx) < FINANCIAL_PRECISION)) {
                    return $x_mid;
                }
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * NPV
         * Returns the Net Present Value of a cash flow series given a discount rate.
         * @return    float
         */
        public static function NPV() {
            // Return value
            $returnValue = 0;
            // Loop through arguments
            $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
            // Calculate
            $rate = array_shift($aArgs);
            for ($i = 1; $i <= count($aArgs); ++$i) {
                // Is it a numeric value?
                if (is_numeric($aArgs[$i - 1])) {
                    $returnValue += $aArgs[$i - 1] / pow(1 + $rate, $i);
                }
            }
            // Return
            return $returnValue;
        }

        /**
         * ISPMT
         * Returns the interest payment for an investment based on an interest rate and a constant payment schedule.
         * Excel Function:
         *     =ISPMT(interest_rate, period, number_payments, PV)
         * interest_rate is the interest rate for the investment
         * period is the period to calculate the interest rate.  It must be betweeen 1 and number_payments.
         * number_payments is the number of payments for the annuity
         * PV is the loan amount or present value of the payments
         */
        public static function ISPMT() {
            // Return value
            $returnValue = 0;
            // Get the parameters
            $aArgs              = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
            $interestRate       = array_shift($aArgs);
            $period             = array_shift($aArgs);
            $numberPeriods      = array_shift($aArgs);
            $principleRemaining = array_shift($aArgs);
            // Calculate
            $principlePayment = ($principleRemaining * 1.0) / ($numberPeriods * 1.0);
            for ($i = 0; $i <= $period; ++$i) {
                $returnValue        = $interestRate * $principleRemaining * -1;
                $principleRemaining -= $principlePayment;
                // principle needs to be 0 after the last payment, don't let floating point screw it up
                if ($i == $numberPeriods) {
                    $returnValue = 0;
                }
            }
            return ($returnValue);
        }

        /**
         * MIRR
         * Returns the modified internal rate of return for a series of periodic cash flows. MIRR considers both
         *        the cost of the investment and the interest received on reinvestment of cash.
         * Excel Function:
         *        MIRR(values,finance_rate, reinvestment_rate)
         * @param    float[] $values                  An array or a reference to cells that contain a series of payments and
         *                                            income occurring at regular intervals.
         *                                            Payments are negative value, income is positive values.
         * @param    float   $finance_rate            The interest rate you pay on the money used in the cash flows
         * @param    float   $reinvestment_rate       The interest rate you receive on the cash flows as you reinvest them
         * @return    float
         */
        public static function MIRR($values, $finance_rate, $reinvestment_rate) {
            if (!is_array($values)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $values            = PHPExcel_Calculation_Functions::flattenArray($values);
            $finance_rate      = PHPExcel_Calculation_Functions::flattenSingleValue($finance_rate);
            $reinvestment_rate = PHPExcel_Calculation_Functions::flattenSingleValue($reinvestment_rate);
            $n                 = count($values);
            $rr = 1.0 + $reinvestment_rate;
            $fr = 1.0 + $finance_rate;
            $npv_pos = $npv_neg = 0.0;
            foreach ($values as $i => $v) {
                if ($v >= 0) {
                    $npv_pos += $v / pow($rr, $i);
                } else {
                    $npv_neg += $v / pow($fr, $i);
                }
            }
            if (($npv_neg == 0) || ($npv_pos == 0) || ($reinvestment_rate <= -1)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $mirr = pow((-$npv_pos * pow($rr, $n)) / ($npv_neg * ($rr)), (1.0 / ($n - 1))) - 1.0;
            return (is_finite($mirr) ? $mirr : PHPExcel_Calculation_Functions::VALUE());
        }

        /**
         * NOMINAL
         * Returns the nominal interest rate given the effective rate and the number of compounding payments per year.
         * @param    float $effect_rate Effective interest rate
         * @param    int   $npery       Number of compounding payments per year
         * @return    float
         */
        public static function NOMINAL($effect_rate = 0, $npery = 0) {
            $effect_rate = PHPExcel_Calculation_Functions::flattenSingleValue($effect_rate);
            $npery       = (int)PHPExcel_Calculation_Functions::flattenSingleValue($npery);
            // Validate parameters
            if ($effect_rate <= 0 || $npery < 1) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            // Calculate
            return $npery * (pow($effect_rate + 1, 1 / $npery) - 1);
        }

        /**
         * NPER
         * Returns the number of periods for a cash flow with constant periodic payments (annuities), and interest rate.
         * @param    float $rate Interest rate per period
         * @param    int   $pmt  Periodic payment (annuity)
         * @param    float $pv   Present Value
         * @param    float $fv   Future Value
         * @param    int   $type Payment type: 0 = at the end of each period, 1 = at the beginning of each period
         * @return    float
         */
        public static function NPER($rate = 0, $pmt = 0, $pv = 0, $fv = 0, $type = 0) {
            $rate = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $pmt  = PHPExcel_Calculation_Functions::flattenSingleValue($pmt);
            $pv   = PHPExcel_Calculation_Functions::flattenSingleValue($pv);
            $fv   = PHPExcel_Calculation_Functions::flattenSingleValue($fv);
            $type = PHPExcel_Calculation_Functions::flattenSingleValue($type);
            // Validate parameters
            if ($type != 0 && $type != 1) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            // Calculate
            if (!is_null($rate) && $rate != 0) {
                if ($pmt == 0 && $pv == 0) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                return log(($pmt * (1 + $rate * $type) / $rate - $fv) / ($pv + $pmt * (1 + $rate * $type) / $rate)) / log(1 + $rate);
            }
            if ($pmt == 0) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return (-$pv - $fv) / $pmt;
        }

        public static function PRICE($settlement, $maturity, $rate, $yield, $redemption, $frequency, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $rate       = (float)PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $yield      = (float)PHPExcel_Calculation_Functions::flattenSingleValue($yield);
            $redemption = (float)PHPExcel_Calculation_Functions::flattenSingleValue($redemption);
            $frequency  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($frequency);
            $basis      = (is_null($basis)) ? 0 : (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            if (is_string($settlement = PHPExcel_Calculation_DateTime::getDateValue($settlement))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (is_string($maturity = PHPExcel_Calculation_DateTime::getDateValue($maturity))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (($settlement > $maturity) || (!self::isValidFrequency($frequency)) || (($basis < 0) || ($basis > 4))) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $dsc = self::COUPDAYSNC($settlement, $maturity, $frequency, $basis);
            $e   = self::COUPDAYS($settlement, $maturity, $frequency, $basis);
            $n   = self::COUPNUM($settlement, $maturity, $frequency, $basis);
            $a   = self::COUPDAYBS($settlement, $maturity, $frequency, $basis);
            $baseYF = 1.0 + ($yield / $frequency);
            $rfp    = 100 * ($rate / $frequency);
            $de     = $dsc / $e;
            $result = $redemption / pow($baseYF, (--$n + $de));
            for ($k = 0; $k <= $n; ++$k) {
                $result += $rfp / (pow($baseYF, ($k + $de)));
            }
            $result -= $rfp * ($a / $e);
            return $result;
        }

        /**
         * COUPDAYSNC
         * Returns the number of days from the settlement date to the next coupon date.
         * Excel Function:
         *        COUPDAYSNC(settlement,maturity,frequency[,basis])
         * @access    public
         * @category  Financial Functions
         * @param    mixed                        settlement    The security's settlement date.
         *                                        The security settlement date is the date after the issue
         *                                        date when the security is traded to the buyer.
         * @param    mixed                        maturity    The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    mixed                        frequency    the number of coupon payments per year.
         *                                        Valid frequency values are:
         *                                        1    Annual
         *                                        2    Semi-Annual
         *                                        4    Quarterly
         *                                        If working in Gnumeric Mode, the following frequency options are
         *                                        also available
         *                                        6    Bimonthly
         *                                        12    Monthly
         * @param    integer                      basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function COUPDAYSNC($settlement, $maturity, $frequency, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $frequency  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($frequency);
            $basis      = (is_null($basis)) ? 0 : (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            if (is_string($settlement = PHPExcel_Calculation_DateTime::getDateValue($settlement))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (is_string($maturity = PHPExcel_Calculation_DateTime::getDateValue($maturity))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (($settlement > $maturity) || (!self::isValidFrequency($frequency)) || (($basis < 0) || ($basis > 4))) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $daysPerYear = self::daysPerYear(PHPExcel_Calculation_DateTime::YEAR($settlement), $basis);
            $next        = self::couponFirstPeriodDate($settlement, $maturity, $frequency, true);
            return PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $next, $basis) * $daysPerYear;
        }

        /**
         * daysPerYear
         * Returns the number of days in a specified year, as defined by the "basis" value
         * @param    integer $year            The year against which we're testing
         * @param   integer  $basis           The type of day count:
         *                                    0 or omitted US (NASD)    360
         *                                    1                        Actual (365 or 366 in a leap year)
         *                                    2                        360
         *                                    3                        365
         *                                    4                        European 360
         * @return    integer
         */
        private static function daysPerYear($year, $basis = 0) {
            switch ($basis) {
                case 0:
                case 2:
                case 4:
                    $daysPerYear = 360;
                    break;
                case 3:
                    $daysPerYear = 365;
                    break;
                case 1:
                    $daysPerYear = (PHPExcel_Calculation_DateTime::isLeapYear($year)) ? 366 : 365;
                    break;
                default:
                    return PHPExcel_Calculation_Functions::NaN();
            }
            return $daysPerYear;
        }

        /**
         * COUPDAYS
         * Returns the number of days in the coupon period that contains the settlement date.
         * Excel Function:
         *        COUPDAYS(settlement,maturity,frequency[,basis])
         * @access    public
         * @category  Financial Functions
         * @param    mixed                        settlement    The security's settlement date.
         *                                        The security settlement date is the date after the issue
         *                                        date when the security is traded to the buyer.
         * @param    mixed                        maturity    The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    mixed                        frequency    the number of coupon payments per year.
         *                                        Valid frequency values are:
         *                                        1    Annual
         *                                        2    Semi-Annual
         *                                        4    Quarterly
         *                                        If working in Gnumeric Mode, the following frequency options are
         *                                        also available
         *                                        6    Bimonthly
         *                                        12    Monthly
         * @param    integer                      basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function COUPDAYS($settlement, $maturity, $frequency, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $frequency  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($frequency);
            $basis      = (is_null($basis)) ? 0 : (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            if (is_string($settlement = PHPExcel_Calculation_DateTime::getDateValue($settlement))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (is_string($maturity = PHPExcel_Calculation_DateTime::getDateValue($maturity))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (($settlement > $maturity) || (!self::isValidFrequency($frequency)) || (($basis < 0) || ($basis > 4))) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            switch ($basis) {
                case 3:
                    // Actual/365
                    return 365 / $frequency;
                case 1:
                    // Actual/actual
                    if ($frequency == 1) {
                        $daysPerYear = self::daysPerYear(PHPExcel_Calculation_DateTime::YEAR($maturity), $basis);
                        return ($daysPerYear / $frequency);
                    }
                    $prev = self::couponFirstPeriodDate($settlement, $maturity, $frequency, false);
                    $next = self::couponFirstPeriodDate($settlement, $maturity, $frequency, true);
                    return ($next - $prev);
                default:
                    // US (NASD) 30/360, Actual/360 or European 30/360
                    return 360 / $frequency;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * COUPNUM
         * Returns the number of coupons payable between the settlement date and maturity date,
         * rounded up to the nearest whole coupon.
         * Excel Function:
         *        COUPNUM(settlement,maturity,frequency[,basis])
         * @access    public
         * @category  Financial Functions
         * @param    mixed                        settlement    The security's settlement date.
         *                                        The security settlement date is the date after the issue
         *                                        date when the security is traded to the buyer.
         * @param    mixed                        maturity    The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    mixed                        frequency    the number of coupon payments per year.
         *                                        Valid frequency values are:
         *                                        1    Annual
         *                                        2    Semi-Annual
         *                                        4    Quarterly
         *                                        If working in Gnumeric Mode, the following frequency options are
         *                                        also available
         *                                        6    Bimonthly
         *                                        12    Monthly
         * @param    integer                      basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    integer
         */
        public static function COUPNUM($settlement, $maturity, $frequency, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $frequency  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($frequency);
            $basis      = (is_null($basis)) ? 0 : (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            if (is_string($settlement = PHPExcel_Calculation_DateTime::getDateValue($settlement))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (is_string($maturity = PHPExcel_Calculation_DateTime::getDateValue($maturity))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (($settlement > $maturity) || (!self::isValidFrequency($frequency)) || (($basis < 0) || ($basis > 4))) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $settlement                       = self::couponFirstPeriodDate($settlement, $maturity, $frequency, true);
            $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity, $basis) * 365;
            switch ($frequency) {
                case 1: // annual payments
                    return ceil($daysBetweenSettlementAndMaturity / 360);
                case 2: // half-yearly
                    return ceil($daysBetweenSettlementAndMaturity / 180);
                case 4: // quarterly
                    return ceil($daysBetweenSettlementAndMaturity / 90);
                case 6: // bimonthly
                    return ceil($daysBetweenSettlementAndMaturity / 60);
                case 12: // monthly
                    return ceil($daysBetweenSettlementAndMaturity / 30);
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * COUPDAYBS
         * Returns the number of days from the beginning of the coupon period to the settlement date.
         * Excel Function:
         *        COUPDAYBS(settlement,maturity,frequency[,basis])
         * @access    public
         * @category  Financial Functions
         * @param    mixed                        settlement    The security's settlement date.
         *                                        The security settlement date is the date after the issue
         *                                        date when the security is traded to the buyer.
         * @param    mixed                        maturity    The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    mixed                        frequency    the number of coupon payments per year.
         *                                        Valid frequency values are:
         *                                        1    Annual
         *                                        2    Semi-Annual
         *                                        4    Quarterly
         *                                        If working in Gnumeric Mode, the following frequency options are
         *                                        also available
         *                                        6    Bimonthly
         *                                        12    Monthly
         * @param    integer                      basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function COUPDAYBS($settlement, $maturity, $frequency, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $frequency  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($frequency);
            $basis      = (is_null($basis)) ? 0 : (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            if (is_string($settlement = PHPExcel_Calculation_DateTime::getDateValue($settlement))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (is_string($maturity = PHPExcel_Calculation_DateTime::getDateValue($maturity))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (($settlement > $maturity) || (!self::isValidFrequency($frequency)) || (($basis < 0) || ($basis > 4))) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $daysPerYear = self::daysPerYear(PHPExcel_Calculation_DateTime::YEAR($settlement), $basis);
            $prev        = self::couponFirstPeriodDate($settlement, $maturity, $frequency, false);
            return PHPExcel_Calculation_DateTime::YEARFRAC($prev, $settlement, $basis) * $daysPerYear;
        }

        /**
         * PRICEDISC
         * Returns the price per $100 face value of a discounted security.
         * @param    mixed                        settlement    The security's settlement date.
         *                                        The security settlement date is the date after the issue date when the security is traded to the buyer.
         * @param    mixed                        maturity    The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    int                          discount    The security's discount rate.
         * @param    int                          redemption    The security's redemption value per $100 face value.
         * @param    int                          basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function PRICEDISC($settlement, $maturity, $discount, $redemption, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $discount   = (float)PHPExcel_Calculation_Functions::flattenSingleValue($discount);
            $redemption = (float)PHPExcel_Calculation_Functions::flattenSingleValue($redemption);
            $basis      = (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            //    Validate
            if ((is_numeric($discount)) && (is_numeric($redemption)) && (is_numeric($basis))) {
                if (($discount <= 0) || ($redemption <= 0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity, $basis);
                if (!is_numeric($daysBetweenSettlementAndMaturity)) {
                    //    return date error
                    return $daysBetweenSettlementAndMaturity;
                }
                return $redemption * (1 - $discount * $daysBetweenSettlementAndMaturity);
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * PRICEMAT
         * Returns the price per $100 face value of a security that pays interest at maturity.
         * @param    mixed                        settlement    The security's settlement date.
         *                                        The security's settlement date is the date after the issue date when the security is traded to the buyer.
         * @param    mixed                        maturity    The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    mixed                        issue        The security's issue date.
         * @param    int                          rate        The security's interest rate at date of issue.
         * @param    int                          yield        The security's annual yield.
         * @param    int                          basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function PRICEMAT($settlement, $maturity, $issue, $rate, $yield, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $issue      = PHPExcel_Calculation_Functions::flattenSingleValue($issue);
            $rate       = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $yield      = PHPExcel_Calculation_Functions::flattenSingleValue($yield);
            $basis      = (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            //    Validate
            if (is_numeric($rate) && is_numeric($yield)) {
                if (($rate <= 0) || ($yield <= 0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $daysPerYear = self::daysPerYear(PHPExcel_Calculation_DateTime::YEAR($settlement), $basis);
                if (!is_numeric($daysPerYear)) {
                    return $daysPerYear;
                }
                $daysBetweenIssueAndSettlement = PHPExcel_Calculation_DateTime::YEARFRAC($issue, $settlement, $basis);
                if (!is_numeric($daysBetweenIssueAndSettlement)) {
                    //    return date error
                    return $daysBetweenIssueAndSettlement;
                }
                $daysBetweenIssueAndSettlement *= $daysPerYear;
                $daysBetweenIssueAndMaturity   = PHPExcel_Calculation_DateTime::YEARFRAC($issue, $maturity, $basis);
                if (!is_numeric($daysBetweenIssueAndMaturity)) {
                    //    return date error
                    return $daysBetweenIssueAndMaturity;
                }
                $daysBetweenIssueAndMaturity      *= $daysPerYear;
                $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity, $basis);
                if (!is_numeric($daysBetweenSettlementAndMaturity)) {
                    //    return date error
                    return $daysBetweenSettlementAndMaturity;
                }
                $daysBetweenSettlementAndMaturity *= $daysPerYear;
                return ((100 + (($daysBetweenIssueAndMaturity / $daysPerYear) * $rate * 100)) / (1 + (($daysBetweenSettlementAndMaturity / $daysPerYear) * $yield)) - (($daysBetweenIssueAndSettlement / $daysPerYear) * $rate * 100));
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * PV
         * Returns the Present Value of a cash flow with constant payments and interest rate (annuities).
         * @param    float $rate Interest rate per period
         * @param    int   $nper Number of periods
         * @param    float $pmt  Periodic payment (annuity)
         * @param    float $fv   Future Value
         * @param    int   $type Payment type: 0 = at the end of each period, 1 = at the beginning of each period
         * @return    float
         */
        public static function PV($rate = 0, $nper = 0, $pmt = 0, $fv = 0, $type = 0) {
            $rate = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $nper = PHPExcel_Calculation_Functions::flattenSingleValue($nper);
            $pmt  = PHPExcel_Calculation_Functions::flattenSingleValue($pmt);
            $fv   = PHPExcel_Calculation_Functions::flattenSingleValue($fv);
            $type = PHPExcel_Calculation_Functions::flattenSingleValue($type);
            // Validate parameters
            if ($type != 0 && $type != 1) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            // Calculate
            if (!is_null($rate) && $rate != 0) {
                return (-$pmt * (1 + $rate * $type) * ((pow(1 + $rate, $nper) - 1) / $rate) - $fv) / pow(1 + $rate, $nper);
            }
            return -$fv - $pmt * $nper;
        }

        /**
         * RATE
         * Returns the interest rate per period of an annuity.
         * RATE is calculated by iteration and can have zero or more solutions.
         * If the successive results of RATE do not converge to within 0.0000001 after 20 iterations,
         * RATE returns the #NUM! error value.
         * Excel Function:
         *        RATE(nper,pmt,pv[,fv[,type[,guess]]])
         * @access    public
         * @category  Financial Functions
         * @param    float                        nper        The total number of payment periods in an annuity.
         * @param    float                        pmt            The payment made each period and cannot change over the life
         *                                        of the annuity.
         *                                        Typically, pmt includes principal and interest but no other
         *                                        fees or taxes.
         * @param    float                        pv            The present value - the total amount that a series of future
         *                                        payments is worth now.
         * @param    float                        fv            The future value, or a cash balance you want to attain after
         *                                        the last payment is made. If fv is omitted, it is assumed
         *                                        to be 0 (the future value of a loan, for example, is 0).
         * @param    integer                      type        A number 0 or 1 and indicates when payments are due:
         *                                        0 or omitted    At the end of the period.
         *                                        1                At the beginning of the period.
         * @param    float                        guess        Your guess for what the rate will be.
         *                                        If you omit guess, it is assumed to be 10 percent.
         * @return    float
         **/
        public static function RATE($nper, $pmt, $pv, $fv = 0.0, $type = 0, $guess = 0.1) {
            $nper  = (int)PHPExcel_Calculation_Functions::flattenSingleValue($nper);
            $pmt   = PHPExcel_Calculation_Functions::flattenSingleValue($pmt);
            $pv    = PHPExcel_Calculation_Functions::flattenSingleValue($pv);
            $fv    = (is_null($fv)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($fv);
            $type  = (is_null($type)) ? 0 : (int)PHPExcel_Calculation_Functions::flattenSingleValue($type);
            $guess = (is_null($guess)) ? 0.1 : PHPExcel_Calculation_Functions::flattenSingleValue($guess);
            $rate = $guess;
            if (abs($rate) < FINANCIAL_PRECISION) {
                $y = $pv * (1 + $nper * $rate) + $pmt * (1 + $rate * $type) * $nper + $fv;
            } else {
                $f = exp($nper * log(1 + $rate));
                $y = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv;
            }
            $y0 = $pv + $pmt * $nper + $fv;
            $y1 = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv;
            // find root by secant method
            $i  = $x0 = 0.0;
            $x1 = $rate;
            while ((abs($y0 - $y1) > FINANCIAL_PRECISION) && ($i < FINANCIAL_MAX_ITERATIONS)) {
                $rate = ($y1 * $x0 - $y0 * $x1) / ($y1 - $y0);
                $x0   = $x1;
                $x1   = $rate;
                if (($nper * abs($pmt)) > ($pv - $fv)) {
                    $x1 = abs($x1);
                }
                if (abs($rate) < FINANCIAL_PRECISION) {
                    $y = $pv * (1 + $nper * $rate) + $pmt * (1 + $rate * $type) * $nper + $fv;
                } else {
                    $f = exp($nper * log(1 + $rate));
                    $y = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv;
                }
                $y0 = $y1;
                $y1 = $y;
                ++$i;
            }
            return $rate;
        }

        /**
         * RECEIVED
         * Returns the price per $100 face value of a discounted security.
         * @param    mixed                        settlement    The security's settlement date.
         *                                        The security settlement date is the date after the issue date when the security is traded to the buyer.
         * @param    mixed                        maturity    The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    int                          investment    The amount invested in the security.
         * @param    int                          discount    The security's discount rate.
         * @param    int                          basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function RECEIVED($settlement, $maturity, $investment, $discount, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $investment = (float)PHPExcel_Calculation_Functions::flattenSingleValue($investment);
            $discount   = (float)PHPExcel_Calculation_Functions::flattenSingleValue($discount);
            $basis      = (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            //    Validate
            if ((is_numeric($investment)) && (is_numeric($discount)) && (is_numeric($basis))) {
                if (($investment <= 0) || ($discount <= 0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity, $basis);
                if (!is_numeric($daysBetweenSettlementAndMaturity)) {
                    //    return date error
                    return $daysBetweenSettlementAndMaturity;
                }
                return $investment / (1 - ($discount * $daysBetweenSettlementAndMaturity));
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * SLN
         * Returns the straight-line depreciation of an asset for one period
         * @param    cost           Initial cost of the asset
         * @param    salvage        Value at the end of the depreciation
         * @param    life           Number of periods over which the asset is depreciated
         * @return    float
         */
        public static function SLN($cost, $salvage, $life) {
            $cost    = PHPExcel_Calculation_Functions::flattenSingleValue($cost);
            $salvage = PHPExcel_Calculation_Functions::flattenSingleValue($salvage);
            $life    = PHPExcel_Calculation_Functions::flattenSingleValue($life);
            // Calculate
            if ((is_numeric($cost)) && (is_numeric($salvage)) && (is_numeric($life))) {
                if ($life < 0) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                return ($cost - $salvage) / $life;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * SYD
         * Returns the sum-of-years' digits depreciation of an asset for a specified period.
         * @param    cost           Initial cost of the asset
         * @param    salvage        Value at the end of the depreciation
         * @param    life           Number of periods over which the asset is depreciated
         * @param    period         Period
         * @return    float
         */
        public static function SYD($cost, $salvage, $life, $period) {
            $cost    = PHPExcel_Calculation_Functions::flattenSingleValue($cost);
            $salvage = PHPExcel_Calculation_Functions::flattenSingleValue($salvage);
            $life    = PHPExcel_Calculation_Functions::flattenSingleValue($life);
            $period  = PHPExcel_Calculation_Functions::flattenSingleValue($period);
            // Calculate
            if ((is_numeric($cost)) && (is_numeric($salvage)) && (is_numeric($life)) && (is_numeric($period))) {
                if (($life < 1) || ($period > $life)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                return (($cost - $salvage) * ($life - $period + 1) * 2) / ($life * ($life + 1));
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * TBILLEQ
         * Returns the bond-equivalent yield for a Treasury bill.
         * @param    mixed                settlement    The Treasury bill's settlement date.
         *                                The Treasury bill's settlement date is the date after the issue date when the Treasury bill is traded to the buyer.
         * @param    mixed                maturity    The Treasury bill's maturity date.
         *                                The maturity date is the date when the Treasury bill expires.
         * @param    int                  discount    The Treasury bill's discount rate.
         * @return    float
         */
        public static function TBILLEQ($settlement, $maturity, $discount) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $discount   = PHPExcel_Calculation_Functions::flattenSingleValue($discount);
            //    Use TBILLPRICE for validation
            $testValue = self::TBILLPRICE($settlement, $maturity, $discount);
            if (is_string($testValue)) {
                return $testValue;
            }
            if (is_string($maturity = PHPExcel_Calculation_DateTime::getDateValue($maturity))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                ++$maturity;
                $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity) * 360;
            } else {
                $daysBetweenSettlementAndMaturity = (PHPExcel_Calculation_DateTime::getDateValue($maturity) - PHPExcel_Calculation_DateTime::getDateValue($settlement));
            }
            return (365 * $discount) / (360 - $discount * $daysBetweenSettlementAndMaturity);
        }

        /**
         * TBILLPRICE
         * Returns the yield for a Treasury bill.
         * @param    mixed                settlement    The Treasury bill's settlement date.
         *                                The Treasury bill's settlement date is the date after the issue date when the Treasury bill is traded to the buyer.
         * @param    mixed                maturity    The Treasury bill's maturity date.
         *                                The maturity date is the date when the Treasury bill expires.
         * @param    int                  discount    The Treasury bill's discount rate.
         * @return    float
         */
        public static function TBILLPRICE($settlement, $maturity, $discount) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $discount   = PHPExcel_Calculation_Functions::flattenSingleValue($discount);
            if (is_string($maturity = PHPExcel_Calculation_DateTime::getDateValue($maturity))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            //    Validate
            if (is_numeric($discount)) {
                if ($discount <= 0) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                    ++$maturity;
                    $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity) * 360;
                    if (!is_numeric($daysBetweenSettlementAndMaturity)) {
                        //    return date error
                        return $daysBetweenSettlementAndMaturity;
                    }
                } else {
                    $daysBetweenSettlementAndMaturity = (PHPExcel_Calculation_DateTime::getDateValue($maturity) - PHPExcel_Calculation_DateTime::getDateValue($settlement));
                }
                if ($daysBetweenSettlementAndMaturity > 360) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $price = 100 * (1 - (($discount * $daysBetweenSettlementAndMaturity) / 360));
                if ($price <= 0) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                return $price;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * TBILLYIELD
         * Returns the yield for a Treasury bill.
         * @param    mixed                settlement    The Treasury bill's settlement date.
         *                                The Treasury bill's settlement date is the date after the issue date when the Treasury bill is traded to the buyer.
         * @param    mixed                maturity    The Treasury bill's maturity date.
         *                                The maturity date is the date when the Treasury bill expires.
         * @param    int                  price        The Treasury bill's price per $100 face value.
         * @return    float
         */
        public static function TBILLYIELD($settlement, $maturity, $price) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $price      = PHPExcel_Calculation_Functions::flattenSingleValue($price);
            //    Validate
            if (is_numeric($price)) {
                if ($price <= 0) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                    ++$maturity;
                    $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity) * 360;
                    if (!is_numeric($daysBetweenSettlementAndMaturity)) {
                        //    return date error
                        return $daysBetweenSettlementAndMaturity;
                    }
                } else {
                    $daysBetweenSettlementAndMaturity = (PHPExcel_Calculation_DateTime::getDateValue($maturity) - PHPExcel_Calculation_DateTime::getDateValue($settlement));
                }
                if ($daysBetweenSettlementAndMaturity > 360) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                return ((100 - $price) / $price) * (360 / $daysBetweenSettlementAndMaturity);
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        public static function XIRR($values, $dates, $guess = 0.1) {
            if ((!is_array($values)) && (!is_array($dates))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $values = PHPExcel_Calculation_Functions::flattenArray($values);
            $dates  = PHPExcel_Calculation_Functions::flattenArray($dates);
            $guess  = PHPExcel_Calculation_Functions::flattenSingleValue($guess);
            if (count($values) != count($dates)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            // create an initial range, with a root somewhere between 0 and guess
            $x1 = 0.0;
            $x2 = $guess;
            $f1 = self::XNPV($x1, $values, $dates);
            $f2 = self::XNPV($x2, $values, $dates);
            for ($i = 0; $i < FINANCIAL_MAX_ITERATIONS; ++$i) {
                if (($f1 * $f2) < 0.0) {
                    break;
                } elseif (abs($f1) < abs($f2)) {
                    $f1 = self::XNPV($x1 += 1.6 * ($x1 - $x2), $values, $dates);
                } else {
                    $f2 = self::XNPV($x2 += 1.6 * ($x2 - $x1), $values, $dates);
                }
            }
            if (($f1 * $f2) > 0.0) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $f = self::XNPV($x1, $values, $dates);
            if ($f < 0.0) {
                $rtb = $x1;
                $dx  = $x2 - $x1;
            } else {
                $rtb = $x2;
                $dx  = $x1 - $x2;
            }
            for ($i = 0; $i < FINANCIAL_MAX_ITERATIONS; ++$i) {
                $dx    *= 0.5;
                $x_mid = $rtb + $dx;
                $f_mid = self::XNPV($x_mid, $values, $dates);
                if ($f_mid <= 0.0) {
                    $rtb = $x_mid;
                }
                if ((abs($f_mid) < FINANCIAL_PRECISION) || (abs($dx) < FINANCIAL_PRECISION)) {
                    return $x_mid;
                }
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * XNPV
         * Returns the net present value for a schedule of cash flows that is not necessarily periodic.
         * To calculate the net present value for a series of cash flows that is periodic, use the NPV function.
         * Excel Function:
         *        =XNPV(rate,values,dates)
         * @param    float $rate                   The discount rate to apply to the cash flows.
         * @param          array                   of float    $values     A series of cash flows that corresponds to a schedule of payments in dates.
         *                                         The first payment is optional and corresponds to a cost or payment that occurs at the beginning of the investment.
         *                                         If the first value is a cost or payment, it must be a negative value. All succeeding payments are discounted based on a 365-day year.
         *                                         The series of values must contain at least one positive value and one negative value.
         * @param          array                   of mixed    $dates      A schedule of payment dates that corresponds to the cash flow payments.
         *                                         The first payment date indicates the beginning of the schedule of payments.
         *                                         All other dates must be later than this date, but they may occur in any order.
         * @return    float
         */
        public static function XNPV($rate, $values, $dates) {
            $rate = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            if (!is_numeric($rate)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            if ((!is_array($values)) || (!is_array($dates))) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $values   = PHPExcel_Calculation_Functions::flattenArray($values);
            $dates    = PHPExcel_Calculation_Functions::flattenArray($dates);
            $valCount = count($values);
            if ($valCount != count($dates)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if ((min($values) > 0) || (max($values) < 0)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $xnpv = 0.0;
            for ($i = 0; $i < $valCount; ++$i) {
                if (!is_numeric($values[$i])) {
                    return PHPExcel_Calculation_Functions::VALUE();
                }
                $xnpv += $values[$i] / pow(1 + $rate, PHPExcel_Calculation_DateTime::DATEDIF($dates[0], $dates[$i], 'd') / 365);
            }
            return (is_finite($xnpv)) ? $xnpv : PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * YIELDDISC
         * Returns the annual yield of a security that pays interest at maturity.
         * @param    mixed                        settlement      The security's settlement date.
         *                                        The security's settlement date is the date after the issue date when the security is traded to the buyer.
         * @param    mixed                        maturity        The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    int                          price         The security's price per $100 face value.
         * @param    int                          redemption    The security's redemption value per $100 face value.
         * @param    int                          basis         The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function YIELDDISC($settlement, $maturity, $price, $redemption, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $price      = PHPExcel_Calculation_Functions::flattenSingleValue($price);
            $redemption = PHPExcel_Calculation_Functions::flattenSingleValue($redemption);
            $basis      = (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            //    Validate
            if (is_numeric($price) && is_numeric($redemption)) {
                if (($price <= 0) || ($redemption <= 0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $daysPerYear = self::daysPerYear(PHPExcel_Calculation_DateTime::YEAR($settlement), $basis);
                if (!is_numeric($daysPerYear)) {
                    return $daysPerYear;
                }
                $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity, $basis);
                if (!is_numeric($daysBetweenSettlementAndMaturity)) {
                    //    return date error
                    return $daysBetweenSettlementAndMaturity;
                }
                $daysBetweenSettlementAndMaturity *= $daysPerYear;
                return (($redemption - $price) / $price) * ($daysPerYear / $daysBetweenSettlementAndMaturity);
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * YIELDMAT
         * Returns the annual yield of a security that pays interest at maturity.
         * @param    mixed                        settlement     The security's settlement date.
         *                                        The security's settlement date is the date after the issue date when the security is traded to the buyer.
         * @param    mixed                        maturity       The security's maturity date.
         *                                        The maturity date is the date when the security expires.
         * @param    mixed                        issue          The security's issue date.
         * @param    int                          rate         The security's interest rate at date of issue.
         * @param    int                          price        The security's price per $100 face value.
         * @param    int                          basis        The type of day count to use.
         *                                        0 or omitted    US (NASD) 30/360
         *                                        1                Actual/actual
         *                                        2                Actual/360
         *                                        3                Actual/365
         *                                        4                European 30/360
         * @return    float
         */
        public static function YIELDMAT($settlement, $maturity, $issue, $rate, $price, $basis = 0) {
            $settlement = PHPExcel_Calculation_Functions::flattenSingleValue($settlement);
            $maturity   = PHPExcel_Calculation_Functions::flattenSingleValue($maturity);
            $issue      = PHPExcel_Calculation_Functions::flattenSingleValue($issue);
            $rate       = PHPExcel_Calculation_Functions::flattenSingleValue($rate);
            $price      = PHPExcel_Calculation_Functions::flattenSingleValue($price);
            $basis      = (int)PHPExcel_Calculation_Functions::flattenSingleValue($basis);
            //    Validate
            if (is_numeric($rate) && is_numeric($price)) {
                if (($rate <= 0) || ($price <= 0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $daysPerYear = self::daysPerYear(PHPExcel_Calculation_DateTime::YEAR($settlement), $basis);
                if (!is_numeric($daysPerYear)) {
                    return $daysPerYear;
                }
                $daysBetweenIssueAndSettlement = PHPExcel_Calculation_DateTime::YEARFRAC($issue, $settlement, $basis);
                if (!is_numeric($daysBetweenIssueAndSettlement)) {
                    //    return date error
                    return $daysBetweenIssueAndSettlement;
                }
                $daysBetweenIssueAndSettlement *= $daysPerYear;
                $daysBetweenIssueAndMaturity   = PHPExcel_Calculation_DateTime::YEARFRAC($issue, $maturity, $basis);
                if (!is_numeric($daysBetweenIssueAndMaturity)) {
                    //    return date error
                    return $daysBetweenIssueAndMaturity;
                }
                $daysBetweenIssueAndMaturity      *= $daysPerYear;
                $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC($settlement, $maturity, $basis);
                if (!is_numeric($daysBetweenSettlementAndMaturity)) {
                    //    return date error
                    return $daysBetweenSettlementAndMaturity;
                }
                $daysBetweenSettlementAndMaturity *= $daysPerYear;
                return ((1 + (($daysBetweenIssueAndMaturity / $daysPerYear) * $rate) - (($price / 100) + (($daysBetweenIssueAndSettlement / $daysPerYear) * $rate))) / (($price / 100) + (($daysBetweenIssueAndSettlement / $daysPerYear) * $rate))) * ($daysPerYear / $daysBetweenSettlementAndMaturity);
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * isFirstDayOfMonth
         * Returns a boolean TRUE/FALSE indicating if this date is the first date of the month
         * @param    DateTime $testDate The date for testing
         * @return    boolean
         */
        private static function isFirstDayOfMonth($testDate) {
            return ($testDate->format('d') == 1);
        }
    }
